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- 5.3-2 The random variable X has probability density function - {2(1-x). 0, 5.3-3 f(x) = 0 b probability histogram of the data. 2(1-x). 0≤x≤ 1, otherwise. Graph the probability density function of X. Find and graph the cumulative distribution function of X. Generate 1000 values for X and make an empirical probability histogram of the data. The randomO 31 75% i 2:02 pm exam.ptuk.edu.ps/mod/ 19 احتمالات عبد ال له Let X be a continuous random variable with probability density function -1Q 75.108 The proportion of impurities per batch in a certain type of industrial chemical is a random variable X that has the probability density function 20x³ (1 – x), 01Question Six: Consider a continuous random variable X representing the time taken to assemble a part. The variable X is known to be between 0 and 2 minutes, and its probability density function (pdf),f(x), is given by f(x) =, 0< x< 2 (a) Show it is a valid density function (b) Graph this density function. (c) Find the probability that X is between 1 and 2. (d) Find the mean (or expected value E(X) and the variance for this probability distribution.need help with this thanks3.1 The proportion of time per day that all checkout counters in a Checkers Hypermarket are busy is a random variable Y with a density function given by Oy²(1 – y), 0 < y< 1 %3D 0, elsewhere Find the mean and standard deviation and interpret your answer.Probability and statsQuestion 5 The continuous random variable X has the probability density function (pdf) given by: [k-5+x 5Question 37 and 38.Question 2 The probability density function of the reliability of a piece of equipment is given by: a x)= a(162 – x²³) (x)=(a/1 16-x³ 0SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,